Selected aspects of enzymatic catalytic activity studied by theoretical methods

Selected Aspects of Enzymatic Catalytic Activity Studied by
Theoretical Methods
and
Implementation of the Analytic Second Derivatives of
Hartree-Fock and Hybrid Density Functional Energies

Dissertation

zur
Erlangung des Doktorgrades (Dr. rer. nat.)
der
Mathematisch-Naturwissenschaftlichen Fakultät
der
Rheinischen Friedrich-Wilhelms-Universität Bonn

vorgelegt von

Dmytro Bykov
aus

Kiew

Bonn 2013



 

 

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Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakultät der Rheinischen
Friedrich-Wilhelms-Universität Bonn

1. Gutachter: Prof. Dr. Frank Neese
2. Gutachter: Prof. Dr. Stefan Grimme
Tag der Promotion: 20.12.2013
Erscheinungsjahr: 2014

IN DER DISSERTATION EINGEBUNDEN:
Zusammenfassung


 



 

 

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Моїй родині


 



 

 

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ABSTRACT
This thesis deals with application of modern theoretical methods for studying enzymatic reactivity
as well as with the efficient implementation of second analytical energy derivatives on the selfconsistent field (SCF) theory level. The enzymatic mechanisms are investigated in the framework of
electronic structure theory with special accent put on kinetics, proton-coupled electron transfer and
theoretical support of EPR and Mössbauer experiments. The theory part of the thesis includes
conventional implementation of SCF second derivatives into ORCA set of programs combined with
efficient approximations like “resolution of identity” and chain of spheres. The results of present
work are divided into six chapters 3.1-3.6, each dealing with different aspects of the aforementioned
subjects. In the following the content of each chapters will be briefly outlined.
The chapters 3.1-3.3 are dedicated to cytochrome c nitrite reductase (CcNiR) enzyme mechanism.
CcNiR is a homodimeric enzyme, containing five covalently attached c-type hemes per subunit.
Four of the heme-irons are bis-histidine ligated, while the fifth, the active site of the protein, has an
unusual lysine coordination and calcium site nearby. A fascinating feature of this enzyme is that the
full six-electron reduction of the nitrite to ammonia is achieved without release of any detectable
reaction intermediate.
In chapter 3.1 the possible role of second-sphere active site amino acids as proton donors is
investigated by taking different possible protonation states and geometrical conformations into
account. It was found that the most probable proton donor is His277, whose spatial orientation and
fine-tuned acidity lead to energetically feasible, low-barrier protonation reactions. However,
substrate protonation may also be accomplished by Arg114. The calculated barriers for the Arg114
pathway are only slightly higher than the experimentally determined value of 15.2 kcal/mol for the
rate-limiting step.
Chapter 3.2 presents the study of the active site reactivation with protons and electrons modeled by
the series of reaction intermediates based on nitrogen monoxide (Fe(II)-NO+, Fe(II)-NO•, Fe(II)NO- and Fe(II)-HNO). The activation barriers for the various proton and electron transfer steps
were estimated in the framework of Marcus theory. Using the obtained barriers, the kinetics of the
reduction process was simulated. It was found that the complex reactivation process can be
accomplished in two possible ways: either through two consecutive proton coupled electron

transfers (PCET) or in the form of three consecutive elementary steps involving reduction, PCET
and protonation. Kinetic simulations revealed the recharging through two PCETs to be a means of
overcoming the predicted deep energetic minimum that is calculated to occur at the stage of the
Fe(II)-NO• intermediate.
In chapter 3.3 the second half cycle of the nitrite reduction catalyzed by CcNiR was considered in
details. In total 3 electrons and 4 protons must be provided to reach the final product ammonia
starting form HNO intermediate. The first event in this half cycle is the reduction of the HNO
intermediate accomplished by PCET reaction. The isomeric intermediates HNOH• and H2NO• are
formed. Both intermediates are active and are readily transformed into hydroxylamine most likely
through intramolecular proton transfer either from Arg114 or His277. The protonated side chain then

 



 

 

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provides its proton to initiate a heterolytic cleavage reaction of the N-O bond. As a result the H2N+
intermediate is formed. The latter readily picks up an electron forming H2N+•, which in turn reacts
with Tyr218. Intramolecular reaction with Tyr218 in the final step of the nitrite reduction process
leads directly to the ammonia final product. The product dissociation was found to proceed through
the change of spin state, which was also observed in resonance Raman investigation of Martins
(Martins, G., et. al. (2010), J Phys Chem B 114, 5563)
Chapter 3.4 is concerned with cd1 nitrite reductase (NIR) enzyme. NIR is a key enzyme in the
denitrification process that reduces nitrite to nitric oxide (NO). There are three residues at the
“distal” side of the active site heme (Tyr10, His327 and His369) and in this work the focus was set on
the identification and characterization of possible H-bonds they can form with the NO, thereby
affecting the stability of the complex. It was shown that the NO in the nitrosyl d1-heme complex of
cd1 NIR forms H-bonds with Tyr10 and His369 whereas the second conserved histidine, His327,
appears to be less involved in NO H-bonding. Moreover, it was shown that the H-bonding network
within the active site is dynamic and that a change in the protonation state of one of the residues
does affect the strength and position of the H-bonds formed by the others. In the Y10F mutant
His369 is closer to the NO, whereas mutation of both distal histidines displaces Tyr10 removing its
H-bond. The implications of the H-bonding network found in terms of the complex stability and
catalysis are discussed.
The electronic structure of the [4Fe-3S] cluster in Hydrogenase I (Hase I) is discussed in chapter
3.5. The cluster performs two redox transitions within a very small potential range, forming a superoxidized state above +200 mV vs SHE. Crystallographic data has revealed that this state is
stabilized by the coordination of one of the iron atoms to a backbone nitrogen. Thus, the proximal
[4Fe-3S] cluster undergoes redox-dependent structural changes to serve multiple purposes beyond
classical electron transfer. The field-dependent 57Fe-Mössbauer and EPR data for Hase I is
presented, which in conjunction with spectroscopically calibrated DFT calculations reveal the
distribution of Fe valences and spin-coupling schemes for the iron-sulfur clusters. The data
demonstrate that the electronic structure of the [4Fe-3S] core in its three oxidation states closely
resembles that of corresponding conventional [4Fe-4S] cubanes, albeit with distinct differences for
some individual iron sites.
The implementation of the SCF energy second derivatives is discussed in chapter 3.6. The second
derivatives of electronic energy are the base for the calculation of force constants, harmonic

vibration frequencies, infra red (IR) and Raman intensities. To speed up the evaluation of the
hessian, in particular the two-electron integrals and their derivatives, the resolution of the identity
(RI) and the Chain of Spheres (COS) approximations can be applied. As part of the present work,
the RI and COS approximations are introduced at various stages of the molecular Hessian
evaluation procedure, e.g., the reference energy calculation, various steps of the coupled-perturbed
SCF procedure, and the final integral derivative evaluation. The performance of the approximations
and possible errors introduced are discussed in details. The applicability of the Hessian program
was also greatly extended by the additional functionality such as effective core potentials (ECP),
Van der Waals corrected second derivatives and QM/MM hessian.


 



 

 

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ZUSAMMENFASSUNG
Diese Dissertation umfasst sowohl die Anwendung moderner, computergestützter Methoden zur
Untersuchung von Enzym-Reaktivitäten als auch eine effiziente Implementierung der analytischen
zweiten Ableitungen der SCF-Energie (SCF vom engl. Self Consistent Field). Die enzymatischen
Mechanismen werden mit Hilfe der Elektronenstrukturtheorie untersucht, wobei der Schwerpunkt
auf der Ermittlung kinetischer Parameter, dem protonengekoppelten Elektronentransfer und der
theoretischen Unterstützung von EPR- und Mössbauer-Experimenten liegt. Der theoretische Teil
der Arbeit beinhaltet die konventionelle Implementierung der zweiten SCF-Ableitungen unter
Berücksichtigung von Näherungen wie „Resolution of the Identity“ und „Chain of Spheres“ in das
Programmpaket ORCA. Die Ergebnisse der vorliegenden Arbeit sind in sechs Kapitel unterteilt
(3.1–3.6), von welchen jedes einzelne unterschiedliche Aspekte der oben genannten Themen
betrachtet. Im Folgenden wird jedes Kapitel kurz zusammengefasst.
Die Kapitel 3.1–3.3 widmen sich dem Mechanismus des Cytochrome c Nitrite Reductase (CcNiR)
Enzyms. CcNiR ist ein homodimeres Enzym, das fünf kovalent verknüpfte Häm c pro Untereinheit
enthält. Vier der Häme sind bis-Histidin-koordiniert, während das fünfte, welches das aktive
Zentrum des Proteins ist, eine ungewöhnliche Lysin-Koordination aufweist und zudem ein
Calcium-Ion in seiner unmittelbaren Umgebung hat. Das besondere Merkmal dieses Enzyms ist,
dass die vollständige sechs-Elektronen-Reduktion des Nitrits zu Ammoniak ohne ein detektierbares
Intermediat verläuft.
In Kapitel 3.1 wird die Fähigkeit der Aminosäuren aus der zweiten Koordinationssphäre des aktiven
Zentrums hinsichtlich möglicher Protonierungen des Edukts untersucht, indem verschiedene
Protonierungsmuster und geometrische Konformationen berücksichtigt werden. Die Aminosäure
His277 wird als vielversprechender Protonendonor identifiziert, da ihre räumliche Orientierung und
feinjustierte Azidität eine energetisch günstige Protonierungsreaktionen mit niedriger
Energiebarriere ermöglichen. Ein weiterer Kandidat für diese Protonierungsreaktion ist die
Aminosäure Arg114. Die berechnete Barriere für den geschwindigkeitsbestimmenden Schritt ist für
die Reaktion mit Arg114 nur geringfügig höher als der experimentell bestimmte Wert von 15,2
kcal/mol.
Kapitel 3.2 beschreibt die Untersuchung der Reaktivierung des aktiven Zentrums mit Protonen und
Elektronen. Die Reaktivierung wird mit einer Reihe von Intermediaten auf der Basis von

Stickstoffmonoxid modelliert (Fe(II)-NO+, Fe(II)-NO•, Fe(II)-NO– and Fe(II)-HNO). Die
Aktivierungsbarrieren für die verschiedenen Proton- und Elektrontransferschritte werden im
Rahmen der Marcus-Theorie bestimmt. Der komplexe Reaktivierungsprozess kann prinzipiell auf
zwei möglichen Wegen stattfinden: entweder durch zwei aufeinanderfolgende protonengekoppelte
Elektronentransfer-Schritte (engl. Proton Coupled Electron Transfer, PCET), oder durch drei
aufeinanderfolgende Elementarreaktionen, die Reduktion, PCET und Protonierung beinhalten.
Kinetische Simulationen zeigen, dass der Reaktivierungsmechanismus über zwei PCET-Schritte
eine Möglichkeit ist, das tiefe energetische Minimum, in dem das Fe(II)-NO• Intermediat liegt, zu
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Im Kapitel 3.3 wird der zweite Teil des von CcNiR katalysierten Nitrit-Reduktionszyklus im Detail
untersucht. Ausgehend vom HNO-Intermediat müssen insgesamt drei Elektronen und vier Protonen
zur Verfügung gestellt werden um das Endprodukt Ammoniak zu erreichen. Der erste Schritt in
diesem Halbzyklus ist die Reduktion des HNO-Intermediats durch PCET-Reaktion. Dabei werden
die isomeren Intermediate HNOH• und H2NO• gebildet. Beide Intermediate sind aktiv und werden
ohne weiteres in Hydroxylamin überführt, wobei der intramolekulare Protonentransfer von Arg114
oder His277 am günstigsten ist. Die protonierte Seitenkette stellt das Proton zur Verfügung, wodurch
die heterolytische N-O-Bindungsspaltung initiiert wird. So wird ein H2N+-Intermediat gebildet,
welches ohne weiteres ein Elektron aufnehmen kann, sodass H2N+* resultiert, welches wiederum
mit Tyr218 reagiert. Im letzten Schritt des Nitrit-Reduktionsprozesses führt die intramolekulare
Reaktion mit Tyr218 direkt zu dem Endprodukt Ammoniak. Die Dissoziation des Produkts verläuft
unter Änderung des Spinzustands, was auch durch Resonanz-Raman Spektroskopie belegt wurde
(Martins, G., et. al. (2010), J Phys Chem B 114, 5563).
Kapitel 3.4 befasst sich mit dem cd1 Nitrit-Reduktase (NIR) Enzym. NIR ist das Schlüsselenzym im
Denitrifizierungsprozess, in dem Nitrit zu Stickstoffmonoxid (NO) reduziert wird. Die drei
Aminosäuren Tyr10, His327 und His369 befinden sich auf einer Seite des Häms im aktiven Zentrum.
In diesem Kapitel liegt das Hauptaugenmerk auf der Identifizierung und Charakterisierung
möglicher Wasserstoffbrückenbindungen, die diese Aminosäuren ausbilden können, da dies die
Stabilität des Komplexes beeinflusst. Das NO im Nitrosyl Häm d1-Komplex bildet
Wasserstoffbrückenbindungen mit Tyr10 und His369, während das zweite konservierte Histidin,
His327, eine geringere Neigung zur Bildung von Wasserstoffbrückenbindungen zeigt. Zudem wird
gezeigt, dass das Wasserstoffbrückennetzwerk im aktiven Zentrum dynamisch ist und die Änderung
des Protonierungszustands eines der Liganden die Stärke und Position der anderen
Wasserstoffbrückenbindungen beeinflusst. In der Y10F Mutante hat His369 einen geringeren
Abstand zu NO, während die Mutation der beiden entfernten Histidin-Seitenketten Tyr10 verschiebt,
sodass eine Wasserstoffbrückenbindung zwischen Tyr10 und Edukt nicht mehr möglich ist. Der
Einfluss des Wasserstoffbrückennetzwerks wird mit Hinblick auf die Stabilität des Komplexes und
den Katalysezyklus diskutiert.
Die Elektronenstruktur des [4Fe-3S]-Clusters in Hydrogenase I (Hase I) wird in Kapitel 3.5
diskutiert. Der Cluster zeigt zwei Redox-Übergänge innerhalb eines sehr kleinen Potentialbereichs

und bildet so einen super-oxidierten Zustand über +200 mV vs. SHE. Eine Kristallstruktur hat
gezeigt, dass dieser Zustand durch die Koordination eines Rückgrat-Stickstoffatoms an ein
Eisenatom stabilisiert wird. Somit durchläuft der [4Fe-3S]-Cluster redox-abhängige
Strukturänderungen, die außer dem Transfer von Elektronen weitere Ziele erfüllen. Feldabhängige
57
Fe-Mössbauer- und EPR-Daten für Hase I werden präsentiert, die in Verbindung mit kalibrierten
DFT-Berechnungen die Verteilung der Fe-Valenzen und die Erstellung von SpinkopplungsSchemata in den Eisen-Schwefel-Clusters mit verschiedenen Oxidationszuständen ermöglichen. Die
Ergebnisse verdeutlichen, dass die Elektronenstruktur des [4Fe-3S]-Clusters in allen drei
Oxidationszuständen den konventionellen [4Fe-4S]-Kubanen stark ähnelt, obwohl spezifische
Unterschiede für einzelne Eisenzentren vorliegen.
Die Implementierung der zweiten Ableitungen der SCF-Energie wird im Kapitel 3.6 diskutiert. Die
zweiten Ableitungen der elektronischen Energie stellen die Grundlage für die Berechnung von
Kraftkonstanten, harmonischen Schwingungsfrequenzen und Intensitäten in Infrarot- und Raman
 



 

 

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Spektren dar. Zur Beschleunigung der Hessian-Evaluierung, insbesondere der Zwei-ElektronenIntegrale und deren Ableitungen, werden die Näherungen “Resolution of the Identity” (RI) und
“Chain of Spheres” (COS) angewandt. Als Teil der vorliegenden Arbeit werden diese Näherungen
an unterschiedlichen Stellen der Hessian-Evaluierung eingeführt, z.B. bei der Berechnung der
Referenzenergie, in der abschließenden Evaluierung der Integral-Ableitungen und in zahlreichen
Schritten der CPSCF Prozedur (vom engl. Coupled Perturbed SCF). Die Leistung der Näherungen
und möglicherweise durch sie erzeugte Abweichungen werden ausführlich diskutiert. Die
Anwendbarkeit des Hessian-Programms wird durch zusätzliche Funktionalitäten erweitert, wie
beispielsweise Pseudopotentiale, van-der-Waals-korrigierte zweite Ableitungen sowie QM/MM
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LIST OF PUBLICATIONS
Publications related to the thesis:
Chapter 3.1:
Bykov, D.; Neese, F. Substrate binding and activation in the active site of cytochrome c nitrite
reductase: a density functional study. J. Biol. Inorg. Chem. (2011) 16:417-430.
(Contribution by DB: All calculations of the electronic structures, data analysis and paper writing)
Chapter 3.2:
Bykov, D., Neese, F. Reductive activation of the heme-iron-nitrosyl intermediate in the reaction

mechanism of Cytochrome c Nitrite Reductase. A theoretical study. J. Biol. Inorg. Chem. (2012),
17(5):741-60.
(Contribution by DB: All calculations of the electronic structures, data analysis and paper writing)
Chapter 3.3:
Bykov, D., Plog, M., Neese, F. The nitroxyl, hydroxylamine and ammonia intermediates in the
reaction cycle of cytochrome c nitrite reductase. A theoretical study. (2013), accepted to JBIC.
(Contribution by DB: All calculations of the electronic structures, data analysis and paper writing)
Chapter 3.4:
Radoul M., Bykov, D., Rinaldo, S., Cutruzzola, F., Neese, F., Goldfarb, D. Dynamic hydrogenbonding network in the distal pocket of the nitrosyl complex of pseudomonas aeruginosa cd1 nitrite
reductase. J. Am. Chem. Soc. (2011) 133(9):3043-3055.
(Contribution by DB: Support of the experimental studies by the electronic structure calculations,
analysis of the calculated data, paper writing)
Chapter 3.5:
Pandelia, M-E., Bykov, D., Izsak, R., Infossi, P., Giudici-Orticoni, M-T., Bill, E., Neese, F., Lubitz,
W. Reply to Mouesca et al.: Electronic structure of the proximal [4Fe-3S] cluster of O2-tolerant
[NiFe] hydrogenases. PNAS (2013), 110(28):2539.
Pandelia, M-E., Bykov, D., Izsak, R., Infossi, P., Giudici-Orticoni, M-T., Bill, E., Neese, F., Lubitz,
W. The electronic structure of the unique [4Fe-3S] cluster in O2-tolerant hydrogenases
characterized by 57Fe Mössbauer and EPR spectroscopy. PNAS (2013), 110(2):483-488.
(Contribution by DB: Support of the experimental studies by the electronic structure calculations,
analysis of the calculated data, paper writing)


 



 

 

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Chapter 3.6:
Bykov, D., Petrenko, T., Izsak, R., Kossmann, S., Becker U., Valeev, E., Neese, F. Analytic second
derivatives of Hartree-Fock and hybrid DFT energies. A detailed analysis of different
approximations. (2013), to be submitted to JCP.
(Contribution by DB: Leading programmer of the project, running test calculations, data analysis
and paper writing)

Publications by the Author not related to the thesis:
Bykov, D. A., Zaderko, A. N., Datsyuk, A. M., Diyuk, V. E., Yatsimirskii, V. K., Lobanov, V. V.
Quantum-chemical modelling of the reactivity of charcoal surface double bonds. Theoretical and
Experimental Chemistry (2008), 44(1), 32-36.
Chekhovskii, A., Tomila, T., Ragulya, A., Timofeeva, I., Ivanchuk, A., Bykov, D., Labunets, T.
Kinetics of CxNy formation on electrode surface through electrochemical method. Science of
Sintering (2007), 39(3), 287-294.


 

 

 

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ACKNOWLEDGEMENTS
It is my great pleasure to thank those who contributed to my PhD thesis over the years in Bonn and
in Mülheim. There were various scientists from whom I had the opportunity and pleasure to learn
from. They all guided me to some extent through my PhD time:
First and most important, I want to express my deep gratitude to my scientific supervisor Prof.
Frank Neese, who gave me the opportunity to work in the fields of bioinorganic and theoretical
chemistry. Prof. Neese taught me not only the basics of theoretical chemistry but also showed his
attitude and passion to work, became great example of scientific excellence for me. He gave me
freedom and time to work independently and evolve my skills in the subject. Under his guidance I
was working on a variety of projects having great start and support from his site during initial steps
of my scientific career.
I also would like to thank Dr. Taras Petrenko and Dr. Robert Izsak for many scientific discussions.
It was always a pleasure to get explanations with examples from Taras. His deep understanding of

the subject helped me to see the connections between physical picture and mathematical
formulations. Robert was always ready to discuss details on the integral evaluations and
mathematics related questions. We spent a great deal of time reading and discussing the “great pink
book”.
I had a nice and productive research visit to Virginia Tech University and had the opportunity to
work with Prof. Edward Valeev. My sincere thank goes to Ed, who introduced me to the field of
two-electron integrals evaluation and gave a lot of advanced programming tips.
I also wish to thank my collaborators Prof. Wolfgang Lubitz and Prof. Daniella Goldfarb and the
members of their groups Dr. Eckhard Bill, Dr. Maria Pandelia and Dr. Marina Radoul, with whom I
have done highly successful and interesting projects on the interface between experiment and
theory.
Many other people in the physical and theoretical institute in Bonn and in MPI in Mülheim
contributed to a pleasant atmosphere over the last few years. First of all, my warm thanks go to
Claudia Kronz, for her help in setting lots of questions for me upon arrival. I would like to thank my
roommates in Bonn and in Max-Planck institute: Christoph, Shengfa, Michael, Dimitrios, Maylis,
Mahesh. People with whom I had many discussions Dimitriy, DimitriosL, Tobi, Ute, Marius,
Ragnar, Oliver, FrankW. Separate thanks to Igor and Vera for the proofreading. Last, I would like
to express my gratitude to the whole Neese group!
My warm thanks go to my friends who supported me during PhD time. Michailo and Larisa, Irina
and Michail, Lena and Valeriy, Roland, Itana and John, Eugeniy and Olga thanks for being great
friends!
Thanks to all from the “Energy Converters” band! That was a great pleasure to rehears, perform and
have pizza evenings together.
My very special thanks go to my family, who has been supporting me through the whole time of my
PhD studies.
Finally, I want to thank the University of Bonn and Max-Planck society for financial support.


 

 

 

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TABLE OF CONTENTS
Abstract ............................................................................................................................................... V
Zusammenfassung.............................................................................................................................. IX
List of Publications ......................................................................................................................... XIII
Acknowledgements .......................................................................................................................... XV
List of figures ................................................................................................................................... XX
List of tables ...................................................................................................................................XXII
List of abbreviations .................................................................................................................... XXIII
1.

Introduction ................................................................................................................................. 1
1.1 Experimental and Computational Methods in Studying Enzymatic Reactions ................... 1
1.1.1 Overview of the Experimental and Computational Methods............................................ 1

1.1.2 DFT Cluster Approach ..................................................................................................... 2
1.2 Enzymes .................................................................................................................................. 3
1.2.1 Cytochrome C Nitrite Reductase ...................................................................................... 3
1.2.2 cd1 Nitrite Reductase........................................................................................................ 6
1.2.3 Hase 1 Hydrogenase ......................................................................................................... 8
1.3 Analytical Derivatives Method ............................................................................................... 9
1.3.1 Introduction to the Analytical Derivatives Method .......................................................... 9
1.3.2 Approximations in the Hessian Evaluation .................................................................... 10

2.

Methods ...................................................................................................................................... 12
2.1 Calculation of the EPR Parameters with DFT ................................................................... 12
2.1.1 Theory of the EPR in Quantum Chemistry ..................................................................... 12
2.1.2 Calculation of the EPR Spectroscopic Parameters for cd1 NiR .................................... 14
2.2 Electron and Proton Transfer in Enzymes.......................................................................... 14
2.2.1 Marcus Theory and Proton-Coupled Electron Transfer Theory .................................... 14
2.2.2 Calculation of the ET and PT Rates with DFT ............................................................... 16
2.2.3 Calculation of the Standard Redox Potentials and pKa’s............................................... 18
2.3 Mössbauer Parameters Calculations with DFT .................................................................. 19
2.3.1 Theory of Mössbauer Spectroscopy in Quantum Chemistry .......................................... 19
2.3.2 Calculation of the Mössbauer Parameters for Hase 1 Hydrogenase ............................. 20
2.4 Analytical Derivatives Method ............................................................................................. 21
2.4.1 Analytic gradient and hessian of the ground state energy ............................................. 21
2.4.2 Exchange-correlation derivatives with respect to nuclear coordinates ......................... 26
2.4.3 The Resolution of Identity for Analytical Second Derivatives ........................................ 30
2.4.4 The Chain-of-spheres Approximation in Calculation of Hartree-Fock Exchange......... 32

3.

Results ........................................................................................................................................ 37
3.1 Substrate binding and activation in CcNiR ......................................................................... 37
3.1.1 Abstract ........................................................................................................................... 37
3.1.2 Computational Details .................................................................................................... 37
Building up computational model ......................................................................................................................... 37
Computational set up ............................................................................................................................................ 39


 



 

 

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3.1.3 General strategy of the investigation.............................................................................. 39
The scope of the investigation .............................................................................................................................. 39
Setting the energetic reference point in pKa calculations ..................................................................................... 40

3.1.4 Substrate binding ............................................................................................................ 41
Spin State of the Porphyrine Iron.......................................................................................................................... 41
Rest state of the CcNiR enzyme ........................................................................................................................... 43
Nitrite Binding in the active site of the enzyme ................................................................................................... 44
Substrate Back-Bonding in ferrous-nitrite complex ............................................................................................. 45

3.1.5 The N–O bond cleavage. ................................................................................................ 46
Possible pathways for the first N–O bond cleavage based on protonated His277 .................................................. 46
Possible pathways for the first N–O bond cleavage based on deprotonated His277 .............................................. 50
Summary of N–O bond cleavage .......................................................................................................................... 51

3.1.6 Conclusions for the nitrite binding and activation ......................................................... 52
3.2 Reductive activation of the heme-iron-nitrosyl ................................................................... 53
3.2.1 Abstract ........................................................................................................................... 53
3.2.2 Computational details..................................................................................................... 53
Computational model ............................................................................................................................................ 53
Computational details ........................................................................................................................................... 54

3.2.3 Results and discussion .................................................................................................... 55
Geometries ............................................................................................................................................................ 55
Electronic structure, bonding ................................................................................................................................ 58
Calculation of the reference points, pKa and redox potentials. ............................................................................. 62
Reaction energetics ............................................................................................................................................... 64
Modeling of the proton supply .............................................................................................................................. 67
Kinetic barrier calculation..................................................................................................................................... 69

3.2.4 Conclusions .................................................................................................................... 73
3.3 The Nitroxyl, Hydroxylamine and Ammonia Intermediates .............................................. 74
3.3.1 Abstract ........................................................................................................................... 74

3.3.2 Computational model ..................................................................................................... 75
Computational set up ............................................................................................................................................ 75

3.3.3 Results ............................................................................................................................. 76
General strategy .................................................................................................................................................... 76
The HNO intermediate. ......................................................................................................................................... 76
Reactivity of the HNOH and H2NO radical stage. ............................................................................................... 80
Reactivity of the hydroxylamine intermediate and second N-O bond leavage. ................................................... 83
Ammonia stage ..................................................................................................................................................... 85
Dissociation of the final product ........................................................................................................................... 88

3.3.4 Discussion ....................................................................................................................... 89
3.4 Dynamic hydrogen bonding network in the distal pocket of the nitrosyl complex of
Pseudomonas aeruginosa cd1 nitrite reductase ............................................................................ 90
3.4.1 Abstract ........................................................................................................................... 90
3.4.2 Experimental Section ...................................................................................................... 91
Mutagenesis and protein purification .................................................................................................................... 91
Sample Preparation ............................................................................................................................................... 91
Spectroscopic Measurements. ............................................................................................................................... 92
Computational details. .......................................................................................................................................... 93

3.4.3 Experimental Results ...................................................................................................... 94
Echo-Detected EPR .............................................................................................................................................. 94
1
H Davies and 2H Mims ENDOR ......................................................................................................................... 95

3.4.4 Theoretical results .......................................................................................................... 98

 

 

 

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Geometric Structure .............................................................................................................................................. 98
Electronic Structure and Bonding ....................................................................................................................... 100

3.4.5 Calculated EPR parameters ......................................................................................... 102
g-tensor ............................................................................................................................................................... 102
14
N hyperfine couplings of NO and proximal His182 .......................................................................................... 103
Hyperfine couplings of the Tyr10 and His369 protons .......................................................................................... 104

3.4.6 Discussion ..................................................................................................................... 107
3.4.7 Conclusions .................................................................................................................. 109
3.5 The electronic structure of the unique [4Fe-3S] cluster in O2-tolerant hydrogenases
characterized by 57Fe Mössbauer and EPR spectroscopy .......................................................... 110

3.5.1 Abstract ......................................................................................................................... 110
3.5.2 Results ........................................................................................................................... 110
Electric Mössbauer Parameters and Valence States. .......................................................................................... 111
Magnetic Mössbauer Spectra and Spin Distribution. ......................................................................................... 112
Electronic Structure Calculations ....................................................................................................................... 116

3.5.3 Discussion ..................................................................................................................... 118
3.6 The Hessian implementation ............................................................................................. 121
3.6.1 Implementation ............................................................................................................. 121
The program flow ............................................................................................................................................... 121
Van der Waals (VDW) correction ...................................................................................................................... 121
QM/MM hessian ................................................................................................................................................. 122
Effective core potential (ECP) Hessian .............................................................................................................. 123
The COSX implementation................................................................................................................................. 123

3.6.2 Numerical results ......................................................................................................... 124
Computational details ......................................................................................................................................... 124
Integration grids .................................................................................................................................................. 127
Benchmark result: accuracy ................................................................................................................................ 128
Benchmark result: efficiency and timing ............................................................................................................ 131
Benchmark result: representative calculations and parallelization ..................................................................... 134

3.6.3 Conclusions .................................................................................................................. 136
4.

Conclusions .............................................................................................................................. 138
Appendices ................................................................................................................................... 143
A. Contour plots of important MOs calculated under B3LYP/TZV(2d,2p) level of theory for
the (HNO*)HTNA complex ....................................................................................................... 143
B. Calibration of the PBE(a) and B3LYP(b) functionals for the prediction of 57Fe isomer shifts.

.................................................................................................................................................. 144
C1. Statistical analysis of the errors in the calculated vibrational frequencies ( ω ) corresponding
to the ExtremeSCF(ZM) settings, as determined with respect to the results obtained in the
approximation-free ExtremeSCF calculations.......................................................................... 145
C2. Statistical analysis of the differences between the vibrational frequencies ( ω ) calculated
using the SCFConvN and ExtremeSCF(ZN) settings .............................................................. 145
D. The derivatives of the Becke grid weights .......................................................................... 146
Bibliography ................................................................................................................................ 150


 



 

 

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LIST OF FIGURES
Figure 1.1 (a) The overall structure of CcNiR (b) The active site of CcNiR (c) The proposed mechanism ...................... 4
Figure 1.2 The active site of Cytochrome c nitrite reductase (CcNiR) ............................................................................... 5
Figure 1.3 Structures of the [4Fe-3S] cluster of H. marinus hydrogenase, ......................................................................... 9
Figure 3.1 Computational model of the CcNiR active site ............................................................................................... 38
Figure 3.2 Overview of the present investigation on CcNiR ............................................................................................ 41
Figure 3.3 (a) Backbonding interaction of nitrite molecule with ferrous iron (b) The spatial orientation of the NO2substrate molecule ..................................................................................................................................................... 45
Figure 3.4 The charge redistribution in NO2- molecule upon binding to the active site ................................................... 46
Figure 3.5 The conformational potential energy surface of the NO2- (a) and HONO (b) adducts.................................... 47
Figure 3.6 Scheme of the first N–O cleavage ................................................................................................................... 49
Figure 3.7 Potential energy surface of first N–O bond cleavage reaction ........................................................................ 51

Figure 3.8 Computational model for the CcNiR active site. The heme was modeled without its ring substituent .......... 54
Figure 3.9 The optimized structures of the {Fe(NO)}6-{Fe(NO)}8 and {Fe(HNO)}7-{Fe(HNO)}8 complexes ............. 56
Figure 3.10 Contour plots of important MOs. (a) The {Fe(NO)}6 MOs are presented, (b) the {Fe(NO)}7 MOs and (c)
the {Fe(NO)}8 MOs ................................................................................................................................................... 59
Figure 3.11 The model of the bis-histidine-ligated heme 3 .............................................................................................. 62
Figure 3.12 Overall thermodynamic scheme of the recharging process ........................................................................... 64
Figure 3.13 Possible reactions to overcome the kinetic trap (CEH2 complex) ................................................................ 66
Figure 3.14 Optimized structures of the Ca-site models representing part of the inlet channel ....................................... 68
Figure 3.15 The entire recharging process scheme of the CcNiR active site.................................................................... 71
Figure 3.16 Simulated kinetics for both proposed pathways on the basis of the quantum chemical results .................... 72
Figure 3.17 Computational model for the CcNiR active site (taken from pdb structure 2E80) ....................................... 75
Figure 3.18 Contour plots of important MOs for the (HNO)HTHA complex .................................................................... 78
Figure 3.19 Possible protonation and reduction steps starting from (HNO)HT intermediate ........................................... 79
Figure 3.20 Contour plots of important MOs for (HNOH*)HTHA (a) and (H2NO*)HTHA (b) ......................................... 82
Figure 3.21 Possible protonation and reduction steps starting from (HNOH*)HTHA (a) and (H2NO*)HTHA (b)
intermediates ............................................................................................................................................................. 82
Figure 3.22 Contour plots of important MOs for (H2NOH)HTHA .................................................................................... 84
Figure 3.23 Possible protonation and reduction steps starting from (H2NOH)HT intermediate ....................................... 85
Figure 3.24 Contour plots of important MOs for (H2N+)HT and (H2N*)HT ..................................................................... 86
Figure 3.25 Possible protonation and reduction steps starting from (H2N+)HT intermediate. .......................................... 87
Figure 3.26 Dissociation curves for (H3N+*)HA (a) and (H3N+*)HTHA (b) models ......................................................... 88
Figure 3.27 (a) Comparison of W-band ED EPR (8 K) spectra of frozen solutions of WT-NO, Y10F-NO and dHis-NO.
Simulations (magenta) of the spectra of WT-NO (b) and Y10F-NO (c) .................................................................. 95
Figure 3.28 Comparison of orientation selective 1H Davies ENDOR spectra of WT-NO in H2O (black) with 2H Mims
ENDOR spectra of WT-NO in D2O (magenta) at the indicated g values ................................................................. 96
Figure 3.29 Comparison of orientation selective 1H Davies ENDOR spectra of a frozen solution of WT-NO (magenta)
with that of Y10F-NO (black) at the indicated g values ........................................................................................... 97
Figure 3.30 Comparison of the orientation selective 2H Mims ENDOR spectra of WT-NO (magenta) with Y10F-NO
(black) and dHis-NO (blue) at the indicated g values ............................................................................................... 98
Figure 3.31 Calculated geometric parameters of the three selected frozen models (Å and deg). ..................................... 99

Figure 3.32 The SOMO orbital (a) and the spin density (b) of the model A .................................................................. 101
Figure 3.33 Orientation of the g-tensor as obtained from DFT calculations on the frozen structures originating from
1nir........................................................................................................................................................................... 102
Figure 3.34 Experimental (black) and simulated (magenta/blue) 1H Davies ENDOR spectra (a) and 2H Mims ENDOR
spectra (b) of a frozen solution of the WT-NO ....................................................................................................... 105
Figure 3.35 Proposed conformational changes in the distal pocket of the d1-NO complex caused by mutation. .......... 109
Figure 3.36 Zero-field Mössbauer spectra of Hase I recorded at 160 K ......................................................................... 112
Figure 3.37 Magnetic Mössbauer spectra of Hase I (A) reduced with H2 and (B) super-oxidized with air ................... 113


 



 

 

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Figure 3.38 Computational model for the proximal iron-sulfur cluster of the membrane-bound respiratory [NiFe]hydrogenase. ............................................................................................................................................................ 116

Figure 3.39 Week bonding interactions between iron centers in the model Ox2_24 ..................................................... 117
Figure 3.40 Three representative examples for the AnHess program: Penicillin, Plastocyanin model and Vancomycine
................................................................................................................................................................................. 135
Figure 3.41 The parallelization efficiency of the COSX algorithm for the analytical hessian implementation. ............ 136


 



 

 

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LIST OF TABLES
Table 3.1 Relative Energies (kcal/mol) and selected geometric parameters (Å) for Water- and Hydroxyl- complexes of
the active side of CcNiR ............................................................................................................................................ 42
Table 3.2 Energies (kcal/mol) and Selected Geometric Parameters (Å) for the substrate complexes .............................. 44
Table 3.3 Atomic charges (Mulliken analysis), bond lengths (Å) and bond orders of the NO2- substrate molecule in gas

phase and in a bound to ferrous center form. ............................................................................................................ 46
Table 3.4 Selected geometric parameters for the nitrosyl complexes investigated ........................................................... 57
Table 3.5 Mulliken population analysis of the B3LYP densities for the nitrosyl complexes investigated ....................... 61
Table 3.6 The calculated selected geometric parameters (Å) and relative energies of high- and low-spin states (ΔE in
kcal/mol) for the bis-histidine ligated heme model. .................................................................................................. 63
Table 3.7 Calculated adiabatic proton affinities (APA in kcal/mol) and ΔH (kcal/mol) of the water dissociation reaction
in the presence of the Ca-site. ................................................................................................................................... 69
Table 3.8 The estimated values for reorganization energies (kcal/mol) using a combination of electrostatic continuum
modeling and force constant analysis........................................................................................................................ 70
Table 3.9 Selected geometric parameters (distances in Å, angles in degrees and vibrational frequencies in cm-1) for the
HNO derivatives ........................................................................................................................................................ 77
Table 3.10 Selected geometric parameters (distances in Å, angles in degrees and vibrational frequencies in cm-1) for the
HNOH and H2NO radical derivatives ....................................................................................................................... 80
Table 3.11 Selected geometric parameters (distances in Å, angles in degrees and vibrational frequencies in cm-1) for the
hydroxylamine and hydroxylamine radical species .................................................................................................. 83
Table 3.12 Selected geometric parameters (distances in Å) for the Ammonia intermediates .......................................... 85
Table 3.13 The geometric parameters (Å and deg) of models A, B and C ...................................................................... 100
Table 3.14 Binding energies (kcal/mol) and spin population on Fe, N(NO) and O(NO) ............................................... 101
Table 3.15 The DFT calculated g-values of the three models compared with the experimental values. ........................ 102
Table 3.16 DFT (PBE) calculation of the hyperfine (A) and nuclear quadrupole (e2Qq/h) coupling constants (MHz) of
14
N of the NO and proximal His182 ligand ............................................................................................................... 103
Table 3.17 DFT (PBE) calculation of hyperfine (A) and nuclear quadrupole (e2Qq/h) coupling constants (MHz) of
protons of Tyr10 and His369 which are H-bonded to the NO group ......................................................................... 104
Table 3.18 FeS Cofactors and Redox States of Hase I. ................................................................................................... 111
Table 3.19 Mössbauer parameters of the reduced and super-oxidized Hase I obtained from magnetic-field and
temperature dependent measurements..................................................................................................................... 114
Table 3.20 Calculated Mössbauer parameters for the iron sites of the proximal [4Fe-3S] cluster in the reduced and
super-oxidized state ................................................................................................................................................. 118
Table 3.21 Distribution of formal oxidation states in the FeS centers of A. aeolicus Hase I .......................................... 119

Table 3.22 Definition of different ORCA program settings specifying the SCF and CP-SCF convergence criteria
together with associated integral and basis function thresholds, used for monitoring the accuracy and efficiency of
analytic second derivative calculations ................................................................................................................... 125
Table 3.23 Definition of the standard DFT grids included in the ORCA package ......................................................... 127
Table 3.24 Statistical analysis of the errors in the calculated vibrational frequencies ( ω ) corresponding to different
ORCA program settings, as determined with respect to the results obtained in the approximation-free calculations
with the ExtremeSCF settings ................................................................................................................................. 129
Table 3.25 Statistical analysis of the errors in the calculated vibrational frequencies ( ω ) corresponding to different XC
grids, as determined with respect to the results obtained with Grid 7..................................................................... 130
Table 3.26 Statistical analysis of the differences between the vibrational frequencies ( ω ) calculated analytically
(AnFreq) and by the finite-difference methods, NumFreq1 and NumFreq2, using XC grids 4 and 7 ................... 131
Table 3.27 Statistical analysis of the errors in the calculated vibrational frequencies ( ω ) corresponding to different
two-electron flags HESS(i1, i2, i3, i4) , as determined with respect to the results obtained in the approximation-free
calculations with the ExtremeSCF settings ............................................................................................................. 132
Table 3.28 The timings for the AnHess program ............................................................................................................ 134
Table 3.29 The AnHess program timings for three representative examples .................................................................. 135


 



 

 

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LIST OF ABBREVIATIONS
Å
Ångstroem
Arg
Arginine
B3LYP
Becke; 3 parameter; Lee-Yang-Parr
BO
Born-Oppenheimer
BP86
Becke; Perdew; 1986
BS
Broken Symmetry
CAS
Complete Active Space
CAS-CI
Complete Active Space Configuration Interaction
CASSCF
Complete Active Space Self-Sonsistent Field
CC
Coupled Cluster
CcNiR
Cytochrome c Nitrite Reductase

CD
Circular Dichroism
cd1NiR
cd1 Nitrite Reductase
COSMO
Conductor-like Screening Model
CI
Configuration Interaction
CIS
Configuration Interaction with Single excitations
Def2-TZVP(-f)
Definition 2 of Triple-Zeta Valence plus Polarization (-f functions)
DFT
Density Functional Theory
DOMO
Doubly Occupied Molecular Orbital
ECP
Effective Core Potential
EPR
Electron Paramagnetic Resonance
eV
electron-Volt
ET
Electron Transfer
GGA
Generalized Gradient Approximation
GTO
Gaussian-Type Orbital
HF
Hartree-Fock

HS
High Spin
K
Kelvin
LDA
Local Density Approximation
LSD
Local Spin-Density Approximation
PC
Point Charges
PCET
Proton Coupled Electron Transfer
PSII
Photosystem II
PT
Proton Transfer
RHF
Restricted Hartree-Fock
RI
Resolution of the Identity
RIJCOSX
Resolution of the Identity for Coulomb (J-) integrals and Chain of Spheres
for Exchange (X-) integrals
QM
Quantum Mechanics
QM/MM
Quantum Mechanics/Molecular Mechanics
rmsd
root mean square deviation
SCF

Self-Consistent Field

 



 

 
SOMO
TD-DFT
TS
TZVP
UHF
UV/Vis
VMO
XC
VDW
ZORA
ZPE

Dissertation
 


 

 

Singly Occupied Molecular Orbital

Time-Dependent Density Functional Theory
Transition State
Triple-Zeta Valence plus Polarization
Unrestricted Hartree-Fock
Ultraviolet and Visible part of the electromagnetic spectrum
Virtual Molecular Orbital
Exchange-Correlation
Van der Waals
Zero’th Order Regular Approximation
Zero Point Energy


 

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1.

Introduction
 


 

 

1
 

INTRODUCTION

Enzymes are biological macromolecules that catalyze chemical reactions in a living cell.1 The
variety of the catalyzed processes and efficiency in reaction acceleration is a striking feature of
these macromolecular substances. For instance, in case of urease, an enzyme that speeds up the urea
hydrolysis, the acceleration amounts to ~1014 in comparison to the reaction in aqueous solution.2
Enzymes that contain metal ions in their structure are called metalloenzymes. This class of
enzymes, in vast majority of cases, is involved into catalysis of redox reactions.3 Probably the most
prominent and complex metalloenzyme is Photosystem II. The enzyme catalyzes the process of
photosynthesis, which is of central importance for life on our platen.4
Understanding of the enzymatic activity on molecular level takes one of the central roles in
contemporary biochemical research. A wide range of modern spectroscopy and computational
methods pursues this goal. A brief overview of available experimental and computational technics
is given below.

1.1
1.1.1

Experimental and Computational Methods in Studying Enzymatic Reactions
Overview of the Experimental and Computational Methods

Rapid progress in studying enzymatic catalytic activity has been achieved owing to the
development of spectroscopy methods. The major step forward was the determination of the threedimensional structure of myoglobin utilizing X-Ray spectroscopy.5 This work for the first time
made it possible to correlate structural information with enzymatic functionality. Nowadays the

protein data bank6 contains almost 90 000 structures (as of Tuesday Apr 02, 2013 at 5 PM PDT
there were 89393 Structures). The protein structure analysis studies are also supported by nuclear
magnetic resonance (NMR) spectroscopy.7 Though the NMR method has been developing several
decades it is less used than the X-Ray analysis.
Special attention in studying metalloproteins must be paid to spectroscopy methods used to probe
specific regions in the entire protein structure (so called cofactors, prosthetic groups, active sites).
These special sites are of particular interest because the enzymatic catalytic activity often almost
entirely depends on them. For example, prosthetic groups are the binding sites for the substrates,
take part in electron and proton supply, activate and transform the substrate molecules. Gaining
understanding of the active site functionality is a key ingredient in studying enzymatic catalytic
activity. Spectroscopy methods like electron paramagnetic resonance (EPR),8 resonance Raman
(rR),9,10 magnetic circular dichroism (MCD)11 and Mössbauer spectroscopy12,13 are often the only
source of information on structural and electronic features of short-living active site intermediates.